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…or describe it by its bases, non-bases or lines
Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id.
Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as
123 145. Lines are the lines with at least three points of a simple rank-3 matroid.
A revlex encoding is a string of * and 0.
5,849,183 matroids, showing 21,801–21,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.182541 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.182543 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182665 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182700 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182705 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.182737 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.182738 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.182740 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182741 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182747 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182748 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182750 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182751 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182757 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182758 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182761 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182763 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182892 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182936 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182937 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182939 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182940 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182945 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182947 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182948 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182972 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182977 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182984 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.182985 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182988 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182990 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183125 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183126 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183128 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183129 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183167 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183173 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183175 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183176 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.183199 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183206 | 3 | 11 | 150 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.183207 | 3 | 11 | 149 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.183210 | 3 | 11 | 151 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.183215 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183218 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183343 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183344 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183346 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.183347 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183399 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |